Kemper was born in Kansas City, Missouri, the second of four children of Dorothy Ann “Dotty” (Jannarone) and David Woods Kemper, a son of one of the wealthiest families in Missouri. Her father was the chairman and CEO of what is today Commerce Bancshares, a bank holding company founded by the Kemper family. She is the granddaughter of Mildred Lane Kemper, namesake of the Mildred Lane Kemper Art Museum at Washington University in St. Louis, and great-great-granddaughter of banker, insurance man, and railroad magnate William Thornton Kemper Sr.
She is the older sister of television writer Carrie Kemper. Kemper is of Italian (from her maternal grandfather), English, French and German ancestry. Kemper was raised and remains a practicing Roman Catholic.
Her family moved to St. Louis when Kemper was five years old. She attended Conway Elementary School in the affluent suburb of Ladue and high school at John Burroughs School, where she developed an interest in theater and improvisational comedy. One of her teachers was actor Jon Hamm, with whom she appeared in a school play.
In 1999, Kemper made her debut at the Veiled Prophet Ball, where she was named the Veiled Prophet Queen of Love and Beauty.
Kemper graduated from Princeton University in 2002 with a Bachelor of Arts degree in English. At Princeton, Kemper was a member of the school’s improv comedy troupe, Quipfire.
She played on the school’s 1998 national championship field hockey team, maintaining she sat on the bench “roughly 97 percent” of the time before moving on in the following year to focus on theatre.
She attended Worcester College, Oxford, where she studied towards a graduate degree in English.